Historically, “cosmology” was
the realm of philosophers.
Thought that an isolated group
of stars would collapse in on
An infinite universe of stars
should collapse into isolated
islands of mass.
A finely tuned universe could be
balanced and static.
General Relativity: viewing gravity
as curved space time (1915).
Einstein thought the universe was
static and unchanging, although
his equations were dynamic.
Added a cosmological constant
term which acts as an repulsive
force, balancing gravity.
He came to the conclusion that
Einstein’s cosmological equations
predicted that the universe
evolved with time, either
expanding or collapsing.
Einstein wrote that Friedmann had
made a mathematical error and
his results were invalid.In 1923,
Einstein retracted his objection
and agreed relativistic universe
Einstein’s Biggest Blunder?
After Friedmann’s work, Einstein threw
away his Cosmological Constant,
calling it his biggest blunder.
The addition of a cosmological
constant term was a completely
legitimate mathematical exercise.
Einstein’s blunder was choosing a
specific value for the cosmological
constant to balance gravity, not its
addition. It was not discarded, just set
In the 1920s, Hubble measured the speeds of nearby
He found nearly all were rushing away from us, with their
velocity increasing with distance, exactly as predicted in the
The distribution of
matter across the
considered at large
Planck time (<10-43s)
Quarks, leptons, particle and anti-particle
Protons and neutrons form/annihilation
results in photons
Expansion results in stretching of photons
and not so many hadrons produced
Expansion and cooling
As we go back in time, the scale factor R(t) goes to zero. This
means the distance between any two objects also goes to zero.
This is the location of the “Big Bang”.
Which Scale Factor?
The shape of the scale factor depends upon the mix of
energies in the universe. Universes only containing
matter slow down over time, while other universes slow
and then accelerate.
Which is our universe?
If mass a curves space-time
then the universe will have
Omega =0 is flat universe
Omega <1 is open universe
Omega > 1 is closed universe
These open, flat,
are known as
The fate of the universe depends on its density. If we
consider the universe as a sphere of radius R then the
matter has both potential and kinetic energy
PE + KE = -GMm/R + 1/2mv2
Can you show that the critical density (to give a flat
universe) is 3v2/8πGR2?
The Future of the Universe
The mix of matter and energy imply that the expansion of the
universe is beginning to accelerate, and in the future, the universe
will dilute and dim.
Friedmann died soon after he published
his work. Georges Lemaitre examined
the equations of cosmology, especially
the point where the scale factor goes to
Running the universe backwards, he
realized that it must have been hotter in
He proposed the “Hot Big Bang” model
of the universe, where the universe was
born in a hot, dense state and has been
cooling and expanding ever since.
Cosmic Microwave Background
Penzias & Wilson won the 1978 Nobel Prize for detecting the cosmic
microwave background radiation.
Mather & Smoot won the 2006 Nobel prize for showing this radiation
has a blackbody spectrum (2.7K) and for revealing that it is not
smoothly distributed over the sky.
Cosmic Microwave Background
While the mean temperature of the sky is 2.7K, some regions are hotter
and some cooler, with a temperature difference of 0.001K.
Where did these temperature differences come from?
Anisotropies in CMB
Supernovae are exploding stars whose true brightness is well
known. Using the Keck and Hubble Space Telescope, we found
supernovae appeared fainter than expected, showing that the
universe does not contain only matter.
A third of the cosmos is
matter, the most of which is
dark (does not radiate, but
we can feel its gravitational
Heavy elements (that’s us!)
make up 0.03% of the
Some mysterious substance,
dark energy, make up 70% of
Orbital speed versus orbital radius
Applying newton’s laws
V α 1/√r
Everywhere we look in the cosmos we see the gravitational
influence of dark matter, from the rotation curves of
galaxies, large scale motions, gravitational lenses, hot gas
in clusters to the evolution of the entire universe.
Is it a physical substance or physical fudge?
It has been proposed that dark matter can decay into normal matter,
with an equal mix of matter and anti-matter. The PAMELA
(http://pamela.roma2.infn.it) space-craft has been searching for the
signal of this additional flux of anti-matter.
What is dark energy?
Well, we know what it isn’t. It isn’t dark or
It has to possess a negative pressure (a
tension) to cause the universe to
With quantum physics, the vacuum is not
empty but seethes with particles popping
in and out of existence. Such a vacuum
possesses precisely the tension of dark
Only problem is that the density is wrong
by a factor of
CMB Hot & Cool Spots
At the time of reionization (when the universe became neutral)
there were regions of slightly higher and slightly lower density.
Where did these come from?
How Big is the Universe?
Given our mix of dark energy and matter, the universe is infinite in
extent, but we can only see the “observable universe”. As time
proceeds, more and more is revealed.
Reproducing Universe: Linde
Some slides taken from a presentation by Prof Geraint Lewis
Sydney Institute for Astronomy,University of Sydney